Selection sort always has O(n^2) performance, quick sort has an extremely rare worst case performance of O(n^2) and usually has O(n*logn) performance, and merge sort always has O(n*logn) performance.
Merge sort will usually have efficiency comparable to quick sort, however merge sort on an average of all cases will perform better than quick sort. This is because quick sort has a rare worst case in which a terrible pivot is chosen each time the list is partitioned. In this worst case, quick sort has to check every single element in the list n times. Selection sort however will always check every element n times, even if the list is already sorted. For these reasons, selection sort is almost always less efficient than quick sort, and definitely less efficient than merge sort.
Therefor, merge sort is the best of these three options to use on large random lists.
